When the patches are available, you need to update, and likely reboot. Mattias Geniar talks about using the following command to find processes depending on libc, any of which could be running the vulnerable code, these are core processes that you probably cannot just cycle without a reboot [1]. For me the listing looks something like this: agetty, auditd, dbus-daem, dhclient, init, master, mysqld, rsyslogd, sshd, udevd, xinetd. Many of these deal with hostnames, so I would want to be sure everything is clean, and the best option is likely a reboot.
lsof | grep libc | awk '{print $1}' | sort | uniq